To solve this equation, we can first simplify it by using the property of logarithms that states (a^(log(a)) = a for a > 0:

(x+1)^(lg(x+1)) = 100(x+1)
=> (x+1)^(lg(x+1)) = 100(x+1)^1
=> (x+1)^(lg(x+1)) = (x+1)^2

Now we can equate the exponents since the bases are the same:

lg(x+1) = 2

Now, we can rewrite this logarithmic equation in exponential form:

10^(lg(x+1)) = 10^2

This simplifies to:

x + 1 = 100

Therefore, the solution to the equation (x+1)^(lg(x+1)) = 100(x+1) is x = 99.